Problem 70 - Chemistry The Central Science In Si Units

Question

True or false: When the temperature of an exothermic reaction increases, the rate constant of the forward reaction decreases, which leads to a decrease in the equilibrium constant, \(K_{c}\).

Step-by-Step Solution

Answer

False. While the equilibrium constant \(K_c\) decreases, the rate constant \(k\) for the forward reaction typically increases with temperature.

Step 1: Understand the Effect of Temperature on Exothermic Reactions

In an exothermic reaction, as temperature increases, the system shifts towards the reactants to absorb the added heat, according to Le Chatelier’s principle. This implies that the equilibrium constant, \(K_c\), which depends on the ratio of product to reactant concentrations, would decrease.

Step 2: Examine the Rate Constant's Temperature Dependence

The rate constant \(k\) is related to temperature and activation energy by the Arrhenius equation, \(k = Ae^{-Ea/RT}\). For most reactions, increasing temperature increases \(k\), but for exothermic reactions, this may affect the forward and reverse reactions differently.

Step 3: Determine the Equilibrium Constant's Relation to Rate Constants

The equilibrium constant \(K_c\) is related to the rate constants of the forward \(k_f\) and reverse \(k_r\) reactions, \(K_c = \frac{k_f}{k_r}\). As temperature increases, \(k_f\) often increases, but \(k_r\) increases too, which may reduce \(K_c\).

Step 4: Draw Conclusions from Observable Trends

Although increasing temperature generally increases reaction rates, an increase in temperature in exothermic reactions decreases \(K_c\). Therefore, for an exothermic reaction, if temperature is raised, despite \(k_f\) potentially increasing, the equilibrium constant \(K_c\) decreases due to the relative increase in \(k_r\).

Key Concepts

Exothermic Reaction

Understanding exothermic reactions is vital to grasp how temperature changes affect chemical equilibria. In an exothermic reaction, heat is released as products form. Imagine it as a cozy fire creating warmth, where reactants transform to release energy into the surrounding environment. Here’s what happens when temperature changes in such reactions:

• Raising the temperature adds heat to the system, acting as if you’re adding more fuel to the fire.
• The system, according to Le Chatelier’s principle, attempts to counter this "extra fuel" by shifting back towards reactants.
• This shift to reactants means the system absorbs the added heat, aiming to maintain balance.

In essence, an increase in temperature doesn't favor the formation of more products, but rather the reactants due to the attempt to absorb the excess heat.

Le Chatelier's Principle

Le Chatelier's principle helps predict the direction a reaction shifts in response to changes in conditions, such as temperature. Think of it as the reaction's way of saying, "How do I restore balance?" when disturbed. When temperature is increased in an exothermic reaction:

• The reaction shifts away from the heat-producing side, moving towards reactants to absorb and counteract the added heat.
• This response reduces the overall effect of the temperature rise, attempting to re-establish equilibrium.

Thus, Le Chatelier's principle provides insights into why exothermic reactions respond by altering equilibrium concentrations when temperatures rise.

Arrhenius Equation

The Arrhenius equation is a fundamental concept detailing how temperature impacts the rate constant of a chemical reaction. Expressed by \[ k = Ae^{-E_a/RT} \] it shows that the reaction rate constant, \( k \), depends on

• \( A \): A pre-exponential factor relating to frequency of collisions and orientations.
• \( E_a \): Activation energy, the energy barrier for reaction progression.
• \( R \): The universal gas constant.
• \( T \): Temperature in Kelvin; as Temperature (\( T \)) increases, \( k \) generally increases.

However, in exothermic reactions, both forward and reverse reactions experience changes in \( k \). As temperature increases, the forward rate constant \( k_f \) might rise, but the reverse rate constant \( k_r \) can increase even more, affecting the equilibrium constant \( K_c \) and leading to its decrease due to the shifted balance between \( k_f \) and \( k_r \). Understanding this equation is crucial to predict how much reaction rates change with temperature.